I first remember hearing this quote when reading one of Todd Whitaker's books and am certain I have heard it several other places since. I'll be the first to admit, during my first few years of teaching I certainly did not follow this rule. I recall getting so frustrated I would do all three of those things (yell, argue, use sarcasm) with students in my classroom - this was something I touched on when I wrote my PhD dissertation.
But having worked with thousands of different kids in a variety of settings I now realize that adults never win when they show disrespect towards students. Certainly, there may be kids who can handle the criticism and respond favorably to the "tough love," but my experiences have told me that adults should never put down or embarrass students, especially in front of others. Instead, we must always remain calm and find other ways of bringing our concerns to the student's attention. By providing re-direction in a respectful way we salvage the relationship and focus on correcting the behavior moving forward.